Integrodifferential Equations on Time Scales with Henstock-Kurzweil-Pettis Delta Integrals
We prove existence theorems for integro-differential equations 𝑥Δ∫(𝑡)=𝑓(𝑡,𝑥(𝑡),𝑡0𝑘(𝑡,𝑠,𝑥(𝑠))Δ𝑠), 𝑥(0)=𝑥0, 𝑡∈𝐼𝑎=[0,𝑎]∩𝑇, 𝑎∈𝑅+, where 𝑇 denotes a time scale (nonempty closed subset of real numbers 𝑅), and 𝐼𝑎 is a time scale interval. The functions 𝑓,𝑘 are weakly-weakly sequentially continuous with val...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2010/836347 |
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| author | Aneta Sikorska-Nowak |
| author_facet | Aneta Sikorska-Nowak |
| author_sort | Aneta Sikorska-Nowak |
| collection | DOAJ |
| description | We prove existence theorems for integro-differential equations 𝑥Δ∫(𝑡)=𝑓(𝑡,𝑥(𝑡),𝑡0𝑘(𝑡,𝑠,𝑥(𝑠))Δ𝑠), 𝑥(0)=𝑥0, 𝑡∈𝐼𝑎=[0,𝑎]∩𝑇, 𝑎∈𝑅+, where 𝑇 denotes a time scale (nonempty closed subset of real numbers 𝑅), and 𝐼𝑎 is a time scale interval. The functions 𝑓,𝑘 are weakly-weakly sequentially continuous with values in a Banach space 𝐸, and the integral is taken in the sense of Henstock-Kurzweil-Pettis delta integral. This integral generalizes the Henstock-Kurzweil delta integral and the Pettis integral. Additionally, the functions 𝑓 and 𝑘 satisfy some boundary conditions and conditions expressed in terms of measures of weak noncompactness. Moreover, we prove Ambrosetti's lemma. |
| format | Article |
| id | doaj-art-5cf9b721d4e0402396cc245f62a69803 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-5cf9b721d4e0402396cc245f62a698032025-02-03T01:11:24ZengWileyAbstract and Applied Analysis1085-33751687-04092010-01-01201010.1155/2010/836347836347Integrodifferential Equations on Time Scales with Henstock-Kurzweil-Pettis Delta IntegralsAneta Sikorska-Nowak0Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, PolandWe prove existence theorems for integro-differential equations 𝑥Δ∫(𝑡)=𝑓(𝑡,𝑥(𝑡),𝑡0𝑘(𝑡,𝑠,𝑥(𝑠))Δ𝑠), 𝑥(0)=𝑥0, 𝑡∈𝐼𝑎=[0,𝑎]∩𝑇, 𝑎∈𝑅+, where 𝑇 denotes a time scale (nonempty closed subset of real numbers 𝑅), and 𝐼𝑎 is a time scale interval. The functions 𝑓,𝑘 are weakly-weakly sequentially continuous with values in a Banach space 𝐸, and the integral is taken in the sense of Henstock-Kurzweil-Pettis delta integral. This integral generalizes the Henstock-Kurzweil delta integral and the Pettis integral. Additionally, the functions 𝑓 and 𝑘 satisfy some boundary conditions and conditions expressed in terms of measures of weak noncompactness. Moreover, we prove Ambrosetti's lemma.http://dx.doi.org/10.1155/2010/836347 |
| spellingShingle | Aneta Sikorska-Nowak Integrodifferential Equations on Time Scales with Henstock-Kurzweil-Pettis Delta Integrals Abstract and Applied Analysis |
| title | Integrodifferential Equations on Time Scales with Henstock-Kurzweil-Pettis Delta Integrals |
| title_full | Integrodifferential Equations on Time Scales with Henstock-Kurzweil-Pettis Delta Integrals |
| title_fullStr | Integrodifferential Equations on Time Scales with Henstock-Kurzweil-Pettis Delta Integrals |
| title_full_unstemmed | Integrodifferential Equations on Time Scales with Henstock-Kurzweil-Pettis Delta Integrals |
| title_short | Integrodifferential Equations on Time Scales with Henstock-Kurzweil-Pettis Delta Integrals |
| title_sort | integrodifferential equations on time scales with henstock kurzweil pettis delta integrals |
| url | http://dx.doi.org/10.1155/2010/836347 |
| work_keys_str_mv | AT anetasikorskanowak integrodifferentialequationsontimescaleswithhenstockkurzweilpettisdeltaintegrals |